Three-dimensional Korteweg-de Vries equation and traveling wave solutions
type: Item
instance of: scholarly article
title: Three-dimensional Korteweg-de Vries equation and traveling wave solutions
zbMATH Open document ID: 0963.35169
DOI: 10.1155/S0161171200004440
author: Kenneth L. Jones
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2000-12-21T00:00:00Z
full work available at URL: https://eudml.org/doc/48778
review text: Summary: The three-dimensional power Korteweg-de Vries equation \[ [u_t+ u^n u_x+ u_{xxx}]_x+ u_{yy}+ u_{zz}= 0, \] is considered. Solitary wave solutions for any positive integer \(n\) and cnoidal wave solutions for \(n=1\) and \(n=2\) are obtained. The cnoidal wave solutions are shown to be represented as infinite sums of solitons by using Fourier series expansions and Poisson's summation formula.
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 35Q51
Mathematics Subject Classification ID: 76B25
zbMATH DE Number: 1548200
zbMATH Keywords: traveling wave solutions
zbMATH Keywords: solitary wave solutions
zbMATH Keywords: power Korteweg-de Vries equation
zbMATH Keywords: cnoidal wave solutions
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1548200